Solve x^3-9x/x^2+10x+21*x^2+7x/x^2+5x-24

$$\frac { x ^ { 3 } - 9 x } { x ^ { 2 } + 10 x + 21 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 5 x - 24 }$$

Evaluate

$$\frac{x^{2}}{x+8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}-9x}{x^{2}+10x+21}.

$$\frac{x\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+7\right)}\times \frac{x^{2}+7x}{x^{2}+5x-24}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x\left(x-3\right)}{x+7}\times \frac{x^{2}+7x}{x^{2}+5x-24}$$

Multiply \frac{x\left(x-3\right)}{x+7} times \frac{x^{2}+7x}{x^{2}+5x-24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x-3\right)\left(x^{2}+7x\right)}{\left(x+7\right)\left(x^{2}+5x-24\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(x+7\right)x^{2}}{\left(x-3\right)\left(x+7\right)\left(x+8\right)}$$

Cancel out \left(x-3\right)\left(x+7\right) in both numerator and denominator.

$$\frac{x^{2}}{x+8}$$

Expand

$$\frac{x^{2}}{x+8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}-9x}{x^{2}+10x+21}.

$$\frac{x\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+7\right)}\times \frac{x^{2}+7x}{x^{2}+5x-24}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x\left(x-3\right)}{x+7}\times \frac{x^{2}+7x}{x^{2}+5x-24}$$

Multiply \frac{x\left(x-3\right)}{x+7} times \frac{x^{2}+7x}{x^{2}+5x-24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x-3\right)\left(x^{2}+7x\right)}{\left(x+7\right)\left(x^{2}+5x-24\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(x+7\right)x^{2}}{\left(x-3\right)\left(x+7\right)\left(x+8\right)}$$

Cancel out \left(x-3\right)\left(x+7\right) in both numerator and denominator.

$$\frac{x^{2}}{x+8}$$